Sending data to OpenAI to train a new model on does not feel like it constitutes 'AI doesn't forget'. The AI has nothing to do with the thousands of other companies storing your data for various reasons.
You can program a harness to always send a MEMORY.md file like OpenClaw, or use Vector Stores like OpenAI does, or find some other implementation of 'memory', but these are not an inherent feature of 'AI'. Quite the opposite...the LLMs we currently see will never learn or adapt by themselves, they don't touch their own weights